© 2011

Classical Summation in Commutative and Noncommutative L<sub>p</sub>-Spaces


Part of the Lecture Notes in Mathematics book series (LNM, volume 2021)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Andreas Defant
    Pages 1-13
  3. Andreas Defant
    Pages 15-78
  4. Andreas Defant
    Pages 79-158
  5. Back Matter
    Pages 159-173

About this book


The aim of this research is to develop a systematic scheme that makes it possible to transform important parts of the by now classical theory of summation of general orthonormal series into a similar theory for series in noncommutative $L_p$-spaces constructed over a noncommutative measure space (a von Neumann algebra of operators acting on a Hilbert space  together with a faithful normal state on this algebra).


46-XX; 47-XX Menchoff-Rademacher type theorems noncommutative $L_p$-spaces pointwise convergence of orthonormal series summation methods of orthonormal series symmetric spaces of operators

Authors and affiliations

  1. 1.Department of MathematicsCarl von Ossietzky University OldenburgOldenburgGermany

Bibliographic information

Industry Sectors
Finance, Business & Banking
IT & Software


From the reviews:

“The book under review is a beautiful and original exposition on the topic of almost everywhere convergent orthonormal series. … The student or researcher who succeeds in reading this book will be rewarded with a deep understanding of the subject, both in the commutative and noncommutative setting. … the book should stand on the shelf of anyone seriously interested in functional analysis and/or probability.” (Stanisław Goldstein, zbMATH, Vol. 1267, 2013)

“This book is well written, with a concise, clear and readable style. It is divided into 3 chapters and includes a preface, a bibliography consisting of 98 items, and symbol, author and subject indexes. … The book is a good source for specialists and graduate students working in functional analysis and operator theory.” (Mohammad Sal Moslehian, Mathematical Reviews, Issue 2012 d)